Which has a higher value of momentum: $A$ bullet of mass $10 \, g$ moving with a velocity of $400 \, m s^{-1}$ or a cricket ball of mass $400 \, g$ thrown with a speed of $90 \, km h^{-1}$?

$(a)$ $(i)$ Define momentum. State its $SI$ unit.
$(ii)$ An object of mass $50 \ kg$ is accelerated uniformly from a velocity of $4 \ m/s$ to $8 \ m/s$ in $8 \ s$. Find the magnitude of the force exerted on the object.
$(b)$ State Newton's first law of motion.

Why does friction not roll a ball backward if no external force is pushing or pulling it?

Explain the following:
$(i)$ Why does a boatman push the river bank backward with a long bamboo pole when launching his boat into the water?
$(ii)$ Why does a boat tend to leave the shore when passengers are alighting from it? How does the boatman overcome this difficulty?
$(iii)$ Why does a gun recoil when fired?
$(iv)$ How do rockets operate in space?

Using the second law of motion,derive the relation between force and acceleration. $A$ bullet of $10 \, g$ strikes a sandbag at a speed of $10^3 \, m \, s^{-1}$ and gets embedded after traveling $5 \, cm$. Calculate:
$(i)$ The resistive force exerted by the sand on the bullet.
$(ii)$ The time taken by the bullet to come to rest.

State whether the following statement is true or false:
$1 \ N$ is the force that produces an acceleration of $1 \ m \ s^{-2}$ in a body of mass $1 \ g$.